Singularities of Fitzpatrick and convex functions

Dmitry Kramkov, Mihai Sîrbu

Published 2022-12-20Version 1

Zaj\'{\i}\v{c}ek [19] shows that the singularities of a convex function $f$ can be covered by a countable collection of $c-c$ surfaces. We study the geometry of these surfaces and show that their normals are restricted to the cone generated by $F-F$, where $F:= \textrm{cl} \ \textrm{range} \nabla f$. The singularities of projections on monotone sets in pseudo-Euclidean spaces and of the associated Fitzpatrick functions are studied and classified as a case of special interest.